A note on the product of measure algebras
A variant of Alexandrov theorem is proved stating that a compact, subadditive -poset valued mapping is continuous. Then the measure extension theorem is proved for MV-algebra valued measures.
Calculus for observables in a space of functions from an abstract set to the unit interval is developed and then the individual ergodic theorem is proved.
I. Kluvánek suggested to built the Lebesgue integral on a compact interval in the real line by the help of the length of intervals only. In the paper a modification of the Kluvánek construction is presented applicable to abstract spaces, too.
Recently D. Dumitrescu ([4], [5]) introduced a new kind of entropy of dynamical systems using fuzzy partitions ([1], [6]) instead of usual partitions (see also [7], [11], [12]). In this article a representation theorem is proved expressing the entropy of the dynamical system by the entropy of a generating partition.
The paper deals with a new mathematical model for quantum mechanics based on the fuzzy set theory [1]. The indefinite integral of observables is defined and some basic properties of the integral are examined.
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